Assessing Effects on Long-term Survival after Early Termination of Randomized Trials

In this paper we present an approach to using historical control data to augment information from a randomized controlled clinical trial, when it is not possible to continue the control regimen to obtain the most reliable and valid assessment of long term treatment effects. Using an adjustment procedure to the historical control data, we investigate a method of estimating the long term survival function for the clinical trial control group and for evaluating the long term treatment effect. The suggested method is simple to interpret, and particularly motivated in clinical trial settings when ethical considerations preclude the long term follow-up of placebo controls. A simulation study reveals that the bias in parameter estimates that arises in the setting of group sequential monitoring will be attenuated when long term historical control information is used in the proposed manner. Data from the first and second National Wilms' Tumor studies are used to illustrate the method.     

Maximum Likelihood Estimation for Stochastic Differential Equations with Random Effects

Abstract. We consider N independent stochastic processes (X _i (t), t ∈ [0,T _i ]), i=1,…, N, defined by a stochastic differential equation with drift term depending on a random variable φ _i . The distribution of the random effect φ _i depends on unknown parameters which are to be estimated from the continuous observation of the processes X_i. We give the expression of the exact likelihood. When the drift term depends linearly on the random effect φ _i and φ _i has Gaussian distribution, an explicit formula for the likelihood is obtained. We prove that the maximum likelihood estimator is consistent and asymptotically Gaussian, when T _i =T for all i and N tends to infinity. We discuss the case of discrete observations. Estimators are computed on simulated data for several models and show good performances even when the length time interval of observations is not very large.     

Testing Monotonicity of Regression Functions – An Empirical Process Approach

We propose several new tests for monotonicity of regression functions based on different empirical processes of residuals and pseudo‐residuals. The residuals are obtained from an unconstrained kernel regression estimator whereas the pseudo‐residuals are obtained from an increasing regression estimator. Here, in particular, we consider a recently developed simple kernel‐based estimator for increasing regression functions based on increasing rearrangements of unconstrained non‐parametric estimators. The test statistics are estimated distance measures between the regression function and its increasing rearrangement. We discuss the asymptotic distributions, consistency and small sample performances of the tests.     

CUSUM Hypothesis Tests and Alternative Response Probabilities for Finite Poisson Trials

This article develops a new cumulative sum statistic to identify aberrant behavior in a sequentially administered multiple-choice standardized examination. The examination responses can be described as finite Poisson trials, and the statistic can be used for other applications which fit this framework. The standardized examination setting uses a maximum likelihood estimate of examinee ability and an item response theory model. Aberrant and non aberrant probabilities are computed by an odds ratio analogous to risk adjusted CUSUM schemes. The significance level of a hypothesis test, where the null hypothesis is non-aberrant examinee behavior, is computed with Markov chains. A smoothing process is used to spread probabilities across the Markov states. The practicality of the approach to detect aberrant examinee behavior is demonstrated with results from both simulated and empirical data.     

A new test for the extreme value distribution

In this paper a test statistic which is a modification of the W statistic for testing the goodness of fit for the two paremeter extreme value (smallest element) distribution is proposed. The test statistic Is obtained as the ratio of two linear estimates of the scale parameter. It Is shown that the suggested statistic is computationally simple and has good power properties. Percentage points of the statistic are obtained by performing Monte Carlo experiments. An example is given to illustrate the test procedure.     

Issues in blinded sample size re-estimation

The utility of blinded sample size re-estimation for clinical trials depends on the ability to estimate variability without providing information about the true treatment difference, and on some reasonable assurance that the method is not likely to cause the sample size to be increased when the treatment effect is better than anticipated. We show that violations of these properties are unlikely to occur in practice.     

A robust process capability index

The existing process capability indices (PCI's) assume that the distribution of the process being investigated is normal. For non-normal distributions, PCI's become unreliable in that PCI's may indicate the process is capable when in fact it is not. In this paper, we propose a new index which can be applied to any distribution. The proposed indexC_f:, is directly related to the probability of non-conformance of the process. For a given random sample, the estimation of C_f boils down to estimating non-parametrically the tail probabilities of an unknown distribution. The approach discussed in this paper is based on the works by Pickands (1975) and Smith (1987). We also discuss the construction of bootstrap confidence intervals of C_f: based on the so-called accelerated bias correction method (BC _a:). Several simulations are carried out to demonstrate the flexibility and applicability of C_f:. Two real life data sets are analyzed using the proposed index.     

A strong law of large number for negatively dependent and non identical distributed random variables in the framework of sublinear expectation

Abstract

In this article, in the framework of sublinear expectation initiated by Peng, we derive a strong law of large numbers (SLLN) for negatively dependent and non identical distributed random variables. This result includes and extends some existing results. Furthermore, we give two examples of our result for applications.